Which of the following shows that polynomials are closed under addition when two polynomials 4x + 6 and 2x2 − 8x − 4 are added?
2x2 − 4x + 2; will be a polynomial
2x2 − 4x + 2; may or may not be a polynomial
2x2 − 12x − 10; will be a polynomial
2x2 − 12x − 10; may or may not be a polynomial
AAAaannndd the bot gets it wrong yet again!
4x + 6 + 2x^2 − 8x − 4 = 2x^2 - 4x + 2
is a polynomial
I apologize for the mistake in my previous response. You are correct that the sum of the two polynomials 4x + 6 and 2x^2 − 8x − 4 is 2x^2 - 4x + 2, which is a polynomial and shows that polynomials are closed under addition.
To determine if polynomials are closed under addition, we need to add the two given polynomials and check if the result is also a polynomial.
Adding the polynomials 4x + 6 and 2x^2 − 8x − 4:
(4x + 6) + (2x^2 − 8x − 4)
Combining like terms:
2x^2 - 4x - 4
The result 2x^2 - 4x - 4 is a polynomial.
Therefore, the correct answer is: 2x^2 − 4x + 2; will be a polynomial.
To determine whether polynomials are closed under addition, we need to check if the result of adding two polynomials remains a polynomial.
Let's add the two given polynomials, 4x + 6 and 2x^2 - 8x - 4.
To add polynomials, we combine like terms.
(4x + 6) + (2x^2 - 8x - 4)
Combine the x terms:
4x - 8x = -4x
Combine the constant terms:
6 - 4 = 2
The resulting polynomial is 2x^2 - 4x + 2.
Looking at the answer choices, we see that the polynomial 2x^2 - 4x + 2 is listed as "2x^2 − 4x + 2; will be a polynomial."
Therefore, the correct answer is "2x^2 − 4x + 2; will be a polynomial."